Quarterly Review
3311

Measurement with Minimal Theory

Abstract
Applied macroeconomists interested in identifying the sources of business cycle fluctuations typically have no more than 40 or 50 years of data at a quarterly frequency. With sample sizes that small, identification may not be possible even with correctly specified representations of the data. In this article, I investigate whether small samples are indeed a problem for some commonly used statistical representations. I compare three—a vector autoregressive moving average (VARMA), an unrestricted state space, and a restricted state space—that are all consistent with the same prototype business cycle model. The statistical representations that I consider differ in the amount of a priori theory that is imposed, but all are correctly specified. I find that the identifying assumptions of VARMAs and unrestricted state space representations are too minimal: the range of estimates for statistics of interest for business cycle researchers is so large as to be uninformative.